I was going through Kullback–Leibler divergence and it was mentioned in the wiki article that it requires absolute continuity. It was written that The Kullback–Leibler divergence is defined only if for all $x$, $Q ( x ) = 0$ implies $P(x)=0$ (absolute continuity). However, I am trying to find a statistical distance that doesn't follow this type of conditions. Thus, $Q(x)$ can be $0$ even though $P(x)$ is not. Is there any type of statistical distance possible without that condition?
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$\begingroup$ You could consider any of the distances that metrize the weak topology. For instance, the Lévy–Prokhorov metric. $\endgroup$– Nate EldredgeJul 30, 2019 at 0:44
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$\begingroup$ @Nate what do you mean by weak topology? $\endgroup$– BikasJul 30, 2019 at 0:47
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$\begingroup$ en.wikipedia.org/wiki/… $\endgroup$– Nate EldredgeJul 30, 2019 at 1:32
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